Barton is on the books of Premier League-bound Burnley at the moment, but his current contract with the Clarets runs out at the end of next month.
Rangers manager Mark Warburton recently told BBC Sport that he wants to sign the former Newcastle United midfielder on a free contract in the summer transfer window.
Former Rangers goalkeeper Goram has urged the Englishman to put pen to paper on a contract with the Scottish Premiership-bound outfit.
Barton was one of the best players for Burnley in the Championship this past season, and he would certainly be an asset for Rangers during the 2016-17 campaign.
The 33-year-old would add bite and experience to Rangers midfield, and that would be important for them in their quest to compete with Old Firm rivals Celtic in the Scottish Premiership.
Rangers could also play in the Europa League next season, as they are in the Scottish Cup final where they will take on Hibernian.